Isometric immersions, energy minimization and self-similar buckling in non-Euclidean elastic sheets

The edges of torn plastic sheets and growing leaves often display hierarchical buckling patterns. We show that this complex morphology i) emerges even in zero strain configurations, and ii) is driven by a competition between the two principal curvatures, rather than between bending and stretching. W...

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Bibliographic Details
Published in:Europhysics letters 2016-04, Vol.114 (2), p.24003-24003
Main Authors: Gemmer, John, Sharon, Eran, Shearman, Toby, Venkataramani, Shankar C.
Format: Article
Language:English
Subjects:
02.40.Hw
46.32.+x
46.70.Hg
Buckling
Curvature
Elastic buckling
Elastic sheets
Immersion
Minimization
Monkeys
Morphology
Plastic buckling
Self-similarity
Sheets
Strain
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Summary:The edges of torn plastic sheets and growing leaves often display hierarchical buckling patterns. We show that this complex morphology i) emerges even in zero strain configurations, and ii) is driven by a competition between the two principal curvatures, rather than between bending and stretching. We identify the key role of branch point (or "monkey saddle") singularities in generating complex wrinkling patterns in isometric immersions, and show how they arise naturally from minimizing the elastic energy.
ISSN:0295-5075
1286-4854
DOI:10.1209/0295-5075/114/24003